In pot, melt butter over medium heat. Sauté garlic and onion until soft. Add rice; sauté for 1 minute. Stir in broth, 1½ cups milk, salt and pepper; bring almost to boil, stirring.
Cover, reduce heat to low, simmer, stirring twice, until rice is almost tender, 20 minutes. Stir in shrimp; cover, simmer for 5 minutes. Stir in remaining milk, then spinach, lemon juice and dill.